Accountability pressures and the Common Core State Standards for Mathematics have created complex demands for educators, especially early-career teachers (ECTs). Analyzing longitudinal data, including the social networks of 119 ECTs, we find that ECTs increase their ambitious mathematics instruction when their network members positively interpret…

We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative…

This article explores the approaches used to plan mathematical reasoning tasks by two peer learning teams, one based in regional Victoria and the other in Vancouver, Canada. The results revealed that planning and peer observation support teachers' knowledge of mathematical reasoning and the pedagogy required to promote it.

This study reports the classroom mathematical practices proposed in an instructional sequence grounding on the principles of inquiry-based learning (IBL) through the use of the dynamic geometry software (DGS) in learning to teach geometric transformations. A 5-week instructional sequence consisting of IBL activities that were guided by the…

The present study attempted to explore the relationship between computational estimation and problem solving in a sample of Year 6 children and adults (N=72). For this purpose, participants were presented with two tasks which asked them to estimate the computational result in eight arithmetic operations (Computational Estimation Task) as well as…

Teachers are continually in search of tasks that balance the dual priorities of rigorous thinking and fluency development. These often-competing priorities are emphasized by national-level organizations as well as by state-level standards and assessments. The National Council of Teachers of Mathematics (NCTM) calls for school mathematics…

The goal of the current study was to investigate the role of executive functions in mathematical creativity. The sample included 278 primary school children (ages 8-13). Two models were compared: the starting model tested whether executive functions (shifting, updating, and inhibition), domain-general creativity, and mathematical ability directly…

Geometry mastery is a must for high school students, affected by several factors such as learning approach (LA), gender, level of basic geometry competencies (BGC) and level of mathematical self-efficacy (MSE) among others. The purpose of this study is to examine those factors that affect the geometry problem solving (GPS) abilities of the…

This article describes several ways to connect probability to other topics within mathematics, over a range of year levels, and across the curriculum. It includes a description of common issues and misconceptions, and practical learning activities to address them.

We explore prospective elementary-school teachers' attempts to provide signs and symbols with mathematical meaning in a case involving non-integers as numerator or denominator. The data comprises 33 responses to a task inquiring about the existence of numbers between 1/6 and 1/7, in which the participants were asked to compose a hypothetical…

Modeling projects in differential equations and engineering courses create an authentic activity and an opportunity to attain the holy grail of "deeper" learning. However, what do we mean by "deeper" learning and how do we create an environment that encourages that? This article describes a proposal and case study in using…

It is generally agreed that good subject knowledge is an important prerequisite for successful teaching. However, what constitutes good subject knowledge is debated, with multiple perspectives taken by policymakers, researchers and schools. This article reports on research into interpretations of 'understanding mathematics in depth' (UMID) of…

The transition to tertiary mathematics requires students to use definitions of mathematical objects instead of intuitions. However, routines of defining and of proving with definitions are difficult to engage in, as they are not familiar to students who come from secondary school mathematics. Defining is highly complex because of its underlying…

Potential benefits of providing elementary school students experiences with coding robots are well-documented. These include building skill sets related to logical thinking, problem solving, persistence, collaboration, and communication (Harrell 2015). The authors embrace the value of coding in helping elementary school students develop these…

This study examined the performance of sixth graders in Hong Kong on a number sense three-tier test (NSTTT) and identified their possible misconceptions about number sense. The NSTTT comprises a content tier, which assesses the content knowledge of number sense; a reason tier, which assesses the reasons for the first-tier responses; and a…